A STUDY ON L-FUZZY NORMAL SUBl-GROUP
|
|
- Griffin Fleming
- 5 years ago
- Views:
Transcription
1 A STUDY ON L-FUZZY NORMAL SUBl-GROUP 1 K.Sunderrajan, 2 A.Senthilkumar and 3 R.Muthuraj 1 SRMV College of Arts and Science, Coimbatore , Tamilnadu, India. 2 SNS College of Technology, Coimbatore , Tamilnadu, India. 3 H.H.The Rajah s College,Pudukkottai-Tamilnadu, India ABSTRACT This paper contains some definitions and results of characteristics. L-fuzzy normal subl -group and its generalized KEYWORDS Fuzzy set, L -fuzzy set, L-fuzzy sub l --group, L-fuzzy normal sub l -group. AMS Subject Classification (2000): 06D72, 06F15, 08A72. 1.INTRODUCTION L. A. Zadeh[11] introduced the notion of fuzzy subset of a set S as a function from X into I = [0, 1]. Rosenfeld[2] applied this concept in group theory and semi group theory, and developed the theory of fuzzy subgroups and fuzzy subsemigroupoids respectively J.A.Goguen [6] replaced the valuations set [0, 1],by means of a complete lattice in an attempt to make a generalized study of fuzzy set theory by studying L-fuzzy sets.. In fact it seems in order to obtain a complete analogy of crisp mathematics in terms of fuzzy mathematics, it is necessary to replace the valuation set by a system having more rich algebraic structure. These concepts l -groups play a major role in mathematics and fuzzy mathematics. G.S.V Satya Saibaba [9] introduced the concept of L- fuzzy sub l -group and L-fuzzy l -ideal of l - group. In this paper, we initiate the study of L-fuzzy normal subl -groups. 2.PRELIMINARIES This section contains some definitions and results to be used in the sequel Definition [5,6,7] A lattice ordered group (l -group) is a system G= (G, *, ) where i (G, *) is a group ii (G, ) is a lattice iii the inclusion is invariant under all translations x a + x+ b i.e. x y a+ x+ b a + y + b, for all a, b G. DOI : /mathsj
2 2.2.Definition [11] Let X be a non-empty set. A fuzzy subset A of X is a function A : X [ 0, 1 ] Definition [1,2] An L-fuzzy subset A of G is called an L-fuzzy subgroup (ALFS) of G if for every x,y G, i ii A(xy ) A(x) A(y) A(x -1 ) = A (x) Definition [9,10] An L-fuzzy subset A of G is said to be an L-fuzzy sub l- group(lfsl ) of G if for any x, y G i. A(xy) A(x) A(y) ii. A(x -1 ) = A(x) iii. A(x y) A(x) A(y) iv. A(x y) A(x) A(y) Definition [4] Let G and G be any two groups. Then the function f: G G is said to be a homomorphism if f (xy) = f (x) f (y) for all x, y in G. 2.6.Definition[3] Let G and G be any two groups (not necessarily commutative). Then the function f: G G is said to be an anti-homomorphism if f (xy) = f (y) f (x) for all x, y in G. Remark: A homomorphism may or may not be an anti-homomorphism 2.7.Definition [8,10] A subl -group H of an l - group G is called a normal subl -group of G if for all x in G and h in H we have xhx -1 H. 2.8.Definition[8,10 ] An L-fuzzy sub l -group A of G is called an L-fuzzy normal sub l -group (LFNSl G) of G if for every x, y G, A(xyx -1 ) A(y). 2
3 3. PROPERTIES OF AN L-FUZZY NORMAL SUB l -GROUP In this section, we discuss properties of an L-fuzzy normal sub l -group 3.1.Theorem Let G be an l-group and A be an L-fuzzy sub l-group of G, then the following conditions are equivalent. i. A is an L-fuzzy normal sub l -group of G. ii. A(xyx -1 ) = A(y), for all x, y G. iii. A(xy) = A(yx), for all x, y G. iv. : i ii. Let A is an L-fuzzy normal sub l -group of G. Then A(xyx -1 ) A(y) for all x, y G. By taking advantage of the arbitrary property of x, we have, A(x -1 y(x -1 ) -1 ) A(y). Now, A(y) = A(x -1 (xyx -1 )(x -1 ) -1 ) = A(xyx -1 ) A(y). Hence, A(xyx -1 ) = A(y) for all x, y G. ii iii. Let A(xyx -1 ) = A(y), for all x, y G. Taking yx instead of y, we get, A(xy ) = A(yx), for all x, y G. iii i. Let A(xy) = A(yx), for all x, y G. A(xyx -1 ) = A(yxx -1 ) = A(y) A(y). Hence, A is an L-fuzzy normal sub l -group of G. 3
4 3.2.Theorem Let A be an L-fuzzy subset of an l -group G. If A(e) = 1 and A(xy -1 ) A(x) A(y), A(x y) A(x) A(y), A(x y) A(x) A(y) and A(xy) = A(yx), for all x and y in G, then A is an L- fuzzy normal sub l -group of a group G, where e is the identity element of G. : Let e be identity element of G and x and y in G. Let A(e) = 1 and A(xy -1 ) A(x) A(y), for all x and y in G. Now, A(x -1 ) = A (ex -1 ) A (e) A (x) 1 A(x) = A(x) Therefore, A(x -1 ) A(x), for all x in G. Hence, A((x -1 ) -1 ) A(x -1 ) and A(x) A(x -1 ). Therefore, A(x -1 ) = A(x), for all x in G. Now, replace y by y -1, then A(xy) = A( x(y -1 ) -1 ) A(x) A(y -1 ) = A(x) A(y), for all x and y in G. A(xy) A(x) A(y), for all x and y in G. Also, we have, A(x y) A(x) A(y), A(x y) A(x) A(y). Hence, A is an L-fuzzy sub l -group of an l -group G. Since, A(xy) = A(yx) for all x and y in G, A is an L-fuzzy normal sub l -group of an l -group G. 3.3.Theorem If A is an L-fuzzy normal sub l -group of an l -group G, then empty or a normal sub l -group of G. H = {x / x G: A(x) = 1} is either It is clear from theorem 3.2 4
5 3.4.Theorem If A is an L-fuzzy normal sub l -group of an l -group G, then H = {x G : A(x) = A(e)} is either empty or a normal sub l -group of G, where e is the identity element of G. Since, H is a sub l -group of G. Now, let for any x in G and y in H, A(xyx -1 ) = A(y) = A(e). Since A is an LFNSl G of an l -group G and y H. Hence, xyx -1 G and H is a normal sub l -group of G. Hence, H is either empty or a normal sub l -group of an l -group G. 3.5.Theorem If A and B are two L-fuzzy normal sub l -groups of an l -group G, then their intersection A B is an L-fuzzy normal sub l -group of G. Let x and y belong to G. i. (A B) (xy) = A(xy) B(xy) { A(x) A(y) } { B(x) B(y) } { A(x) B(x) } { A(y) B(y) } = (A B) (x) (A B) (y). Therefore, (A B) (xy) (A B)(x) (A B) (y), for all x and y in G. ii. (A B)(x -1 ) = A(x -1 ) B(x -1 ) = A(x) B(x) = (A B)(x). Therefore, (A B) (x -1 ) = (A B)(x), for all x in G. iii. (A B) (x y) = A(x y) B(x y) { A(x) A(y) } { B(x) B(y) } { A(x) B(x) } { A(y) B(y) } = (A B) (x) (A B) (y). Therefore, (A B) (x y) (A B)(x) (A B)(y), for all x and y in G. iv. (A B) (x y) = A(x y) B(x y) 5
6 { A(x) A(y) } { B(x) B(y) } { A(x) B(x) } { A(y) B(y) } = (A B) (x) (A B) (y). Therefore, (A B) (x y) (A B)(x) (A B)(y), for all x and y in G. Hence, A B is an L-fuzzy sub l -group of an l -group G. Now, (A B) (xy) = A(xy) B(xy) = A(yx) B(yx), since A and B are LFNSl G of G. = (A B) (yx). (A B) (xy) = (A B) (yx). Hence, A B is an L-fuzzy normal sub l -group of an l -group G. Remark The intersection of a family of L-fuzzy normal sub l-groups of an l -group G is an L-fuzzy normal sub l -group of an l -group G. 3.6.Theorem If A is an L-fuzzy normal sub l-group of an l-group G if and only if A(x) = A(y -1 xy), for all x, y G. Let x and y be in G. Let A be an L-fuzzy normal sub l -group of an l -group G. Now, A(y -1 xy) = A(y -1 yx) = A(ex) = A(x). Therefore, A(x) = A(y -1 xy), for all x and y in G. Conversely, assume that A(x) = A(y -1 xy). Now, A(xy) = A(xyxx -1 ) = A(yx) Therefore, A(xy) = A(yx), for all x and y in G. Hence, A is an L-fuzzy normal sub l -group of an l -group G. 6
7 3.7.Theorem Let A be an L-fuzzy sub l -group of an l -group G with A(y) < A(x), for some x and y in G, then A is an L-fuzzy normal sub l -group of an l -group G. Let A be an L-fuzzy sub l -group of an l -group G. Given A(y) < A(x), for some x and y in G, A(xy) A(x) A(y), as A is an LFSl G of G = A(y); and A(y) = A(x -1 xy) A(x -1 ) A(xy) A(x) A(xy), as A is an LFSl G of G = A(xy). A(y) A(xy) A(y). Therefore, A(xy) = A(y), for all x and y in G. and, A(yx) A(y) A(x), as A is an LFSl G of G = A(y); and A(y) = A(yxx -1 ) A(yx) A(x -1 ) A(yx) A(x), as A is an LFSl G of G = A(yx). A(y) A(yx) A(y). Therefore, A(yx) = A(y), for all x and y in G. Hence, A(xy) = A(y) = A(yx), for all x and y in G. Hence, A(xy) = A(yx), for all x and y in G. Hence, A is an L-fuzzy normal sub l -group of an l -group of G. 3.8.Theorem Let A be an L-fuzzy sub l -group of an l -group G with A(y) > A(x) for some x and y in G, then A is an L-fuzzy normal sub l -group of an l -group G. It is clear from theorem 3.7 7
8 REFERENCES [1] Anthony.J.M, Sherwood.H, A characterization of fuzzy subgroups, Fuzzy sets and systems, 7 (1982), [2] Azriel Rosenfeld, Fuzzy Groups, Journal of mathematical analysis and applications, 35, (1971). [3] Biswas.R, Fuzzy subgroups and anti fuzzy subgroups, Fuzzy Sets and Systems 35 (1990) [4] Choudhury.F.P, Chakraborty.A.B and Khare.S.S, A note on fuzzy subgroups and fuzzy homomorphism, Journal of mathematical analysis and applications, 131, (1988). [5] Garrett Birkhof : Lattice Theory, American Mathematical Society colloquium publications, Volume XXV. [6] J.A. Goguen : L-fuzzy sets, J.Math.Anal.Appl. 18, (1967). [7] V. Murali : Lattice of fuzzy algebras and closure systems in I X, Fuzzy sets and systems 41, (1991). [8] Mukherjee.N.P and Bhattacharya.P : Fuzzy normal subgroups and fuzzy cosets, inform.sci 34 (1984), [9] Satya Saibaba.G.S.V, Fuzzy Lattice Ordered Groups, Southeast Asian Bulletin of Mathematics, 32, (2008). [10] K.Sunderrajan, A.Senthilkumar, Properties of L-fuzzy normal sub -groups, General Mathematical Notes, Vol. 22, No. 1, May 2014, pp [11]L.A. Zadeh : Fuzzy sets, Inform and control, 8, (1965). 8
A STUDY ON ANTI FUZZY SUB-BIGROUP
A STUDY ON ANTI FUZZY SUB-BIGROUP R.Muthuraj Department of Mathematics M.Rajinikannan Department of MCA M.S.Muthuraman Department of Mathematics Abstract In this paper, we made an attempt to study the
More informationA Study on Intuitionistic Multi-Anti Fuzzy Subgroups
A Study on Intuitionistic Multi-Anti Fuzzy Subgroups R.Muthuraj 1, S.Balamurugan 2 1 PG and Research Department of Mathematics,H.H. The Rajah s College, Pudukkotta622 001,Tamilnadu, India. 2 Department
More informationAnti M-Fuzzy Subrings and its Lower Level M-Subrings
ISSN: 2454-132X Impact factor: 4.295 (Volume3, Issue1) Available online at: www.ijariit.com Anti M-Fuzzy Subrings and its Lower Level M-Subrings Nanthini.S. P. Associate Professor, PG and Research Department
More informationON T-FUZZY GROUPS. Inheung Chon
Kangweon-Kyungki Math. Jour. 9 (2001), No. 2, pp. 149 156 ON T-FUZZY GROUPS Inheung Chon Abstract. We characterize some properties of t-fuzzy groups and t-fuzzy invariant groups and represent every subgroup
More informationAnti-Fuzzy Lattice Ordered M-Group
International Journal of Scientific and Research Publications, Volume 3, Issue 11, November 2013 1 Anti-Fuzzy Lattice Ordered M-Group M.U.Makandar *, Dr.A.D.Lokhande ** * Assistant professor, PG, KIT s
More informationThe Homomorphism and Anti-Homomorphism of. Level Subgroups of Fuzzy Subgroups
International Mathematical Forum, 5, 2010, no. 46, 2293-2298 The Homomorphism and Anti-Homomorphism of Level Subgroups of Fuzzy Subgroups K. Jeyaraman Department of Mathematics Alagappa Govt Arts college
More informationAnti Q-Fuzzy Group and Its Lower Level Subgroups
Anti Q-Fuzzy Group and Its Lower Level Subgroups Dr.R.Muthuraj P.M.Sitharselvam M.S.Muthuraman ABSTRACT In this paper, we define the algebraic structures of anti Q-fuzzy subgroup and some related properties
More information- Fuzzy Subgroups. P.K. Sharma. Department of Mathematics, D.A.V. College, Jalandhar City, Punjab, India
International Journal of Fuzzy Mathematics and Systems. ISSN 2248-9940 Volume 3, Number 1 (2013), pp. 47-59 Research India Publications http://www.ripublication.com - Fuzzy Subgroups P.K. Sharma Department
More informationABSTRACT SOME PROPERTIES ON FUZZY GROUPS INTROUDUCTION. preliminary definitions, and results that are required in our discussion.
Structures on Fuzzy Groups and L- Fuzzy Number R.Nagarajan Assistant Professor Department of Mathematics J J College of Engineering & Technology Tiruchirappalli- 620009, Tamilnadu, India A.Solairaju Associate
More informationVAGUE groups are studied by M. Demirci[2]. R.
I-Vague Normal Groups Zelalem Teshome Wale Abstract The notions of I-vague normal groups with membership and non-membership functions taking values in an involutary dually residuated lattice ordered semigroup
More informationHomomorphism and Anti-Homomorphism of an Intuitionistic Anti L-Fuzzy Translation
International Journal of Computer & Organization rends Volume 5 Issue 2 March to pril 2015 Homomorphism and nti-homomorphism of an Intuitionistic nti L-Fuzzy ranslation 1 Dr. P.Pandiammal, 2 L.Vinotha
More informationConstructions of Q-BI Fuzzy Ideals Over Sub Semi- Groups with Respect to (T,S) Norms
International Journal of Computational Science Mathematics. ISSN 0974-3189 Volume 2, Number 3 (2010), pp. 217--223 International Research Publication House http://www.irphouse.com Constructions of Q-BI
More informationA Study on Anti Bipolar Q Fuzzy Normal Semi Groups
Journal of Mathematical Sciences and Applications, 2018, Vol. 6, No. 1, 1-5 Available online at http://pubs.sciepub.com/jmsa/6/1/1 Science and Education Publishing DOI:10.12691/jmsa-6-1-1 A Study on Anti
More informationInterval-valued Fuzzy Normal Subgroups
International Journal of Fuzzy Logic Intelligent Systems, vol.12, no. 3, September 2012, pp. 205-214 http://dx.doi.org/10.5391/ijfis.2012.12.3.205 pissn 1598-2645 eissn 2093-744X Interval-valued Fuzzy
More informationL fuzzy ideals in Γ semiring. M. Murali Krishna Rao, B. Vekateswarlu
Annals of Fuzzy Mathematics and Informatics Volume 10, No. 1, (July 2015), pp. 1 16 ISSN: 2093 9310 (print version) ISSN: 2287 6235 (electronic version) http://www.afmi.or.kr @FMI c Kyung Moon Sa Co. http://www.kyungmoon.com
More information@FMI c Kyung Moon Sa Co.
Annals of Fuzzy Mathematics and Informatics Volume 4, No. 2, October 2012), pp. 365 375 ISSN 2093 9310 http://www.afmi.or.kr @FMI c Kyung Moon Sa Co. http://www.kyungmoon.com On soft int-groups Kenan Kaygisiz
More informationOn Comultisets and Factor Multigroups
Theory and Applications of Mathematics & Computer Science 7 (2) (2017) 124 140 On Comultisets and Factor Multigroups P.A. Ejegwa a,, A.M. Ibrahim b a Department of Mathematics / Statistics / Computer Science,
More informationCollege of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi , China
Applied Mathematics Volume 2013, Article ID 485768, 7 pages http://dx.doi.org/10.1155/2013/485768 Research Article A Study of (λ, μ)-fuzzy Subgroups Yuying Li, Xuzhu Wang, and Liqiong Yang College of Mathematics,
More informationPAijpam.eu THE ZERO DIVISOR GRAPH OF A ROUGH SEMIRING
International Journal of Pure and Applied Mathematics Volume 98 No. 5 2015, 33-37 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v98i5.6
More informationOn Strongly Prime Semiring
BULLETIN of the Malaysian Mathematical Sciences Society http://math.usm.my/bulletin Bull. Malays. Math. Sci. Soc. (2) 30(2) (2007), 135 141 On Strongly Prime Semiring T.K. Dutta and M.L. Das Department
More informationFuzzy Primal and Fuzzy Strongly Primal Ideals
Proceedings of the Pakistan Academy of Sciences 52 (1): 75 80 (2015) Copyright Pakistan Academy of Sciences ISSN: 0377-2969 (print), 2306-1448 (online) Pakistan Academy of Sciences Research Article Fuzzy
More informationA Note on Fuzzy Sets
INFORMATION AND CONTROL 18, 32-39 (1971) A Note on Fuzzy Sets JOSEPH G. BROWN* Department of Mathematics, Virginia Polytechnic Institute, Blacksburg, Virginia 24061 Fuzzy sets are defined as mappings from
More informationSome Properties for M-Homomorphism and M-Anti Homomorphism over Q-Fuzzy M-HX Subgroups and its Level
Journal of Informatics and Mathematical Sciences Vol. 9, No. 1, pp. 73 78, 2017 ISSN 0975-5748 (online); 0974-875X (print) Published by RGN Publications http://www.rgnpublications.com Some Properties for
More informationAnti fuzzy ideal extension of Γ semiring
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874, ISSN (o) 2303-4955 www.imvibl.org /JOURNALS / BULLETIN Vol. 4(2014), 135-144 Former BULLETIN OF THE SOCIETY OF MATHEMATICIANS
More informationOn Certain Generalizations of Fuzzy Boundary
International Mathematical Forum, Vol. 6, 2011, no. 46, 2293-2303 On Certain Generalizations of Fuzzy Boundary Dibyajyoti Hazarika and Debajit Hazarika Department of Mathematical Sciences Tezpur University,
More informationTensor Product of modules. MA499 Project II
Tensor Product of modules A Project Report Submitted for the Course MA499 Project II by Subhash Atal (Roll No. 07012321) to the DEPARTMENT OF MATHEMATICS INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI GUWAHATI
More informationOn Intuitionitic Fuzzy Maximal Ideals of. Gamma Near-Rings
International Journal of Algebra, Vol. 5, 2011, no. 28, 1405-1412 On Intuitionitic Fuzzy Maximal Ideals of Gamma Near-Rings D. Ezhilmaran and * N. Palaniappan Assistant Professor, School of Advanced Sciences,
More informationFUZZY LIE IDEALS OVER A FUZZY FIELD. M. Akram. K.P. Shum. 1. Introduction
italian journal of pure and applied mathematics n. 27 2010 (281 292) 281 FUZZY LIE IDEALS OVER A FUZZY FIELD M. Akram Punjab University College of Information Technology University of the Punjab Old Campus,
More informationTHE notion of fuzzy groups defined by A. Rosenfeld[13]
I-Vague Groups Zelalem Teshome Wale Abstract The notions of I-vague groups with membership and non-membership functions taking values in an involutary dually residuated lattice ordered semigroup are introduced
More informationFuzzy ideals of K-algebras
Annals of University of Craiova, Math. Comp. Sci. Ser. Volume 34, 2007, Pages 11 20 ISSN: 1223-6934 Fuzzy ideals of K-algebras Muhammad Akram and Karamat H. Dar Abstract. The fuzzy setting of an ideal
More informationM-N Anti Fuzzy Normal Soft Groups
Int. J. Math. And Appl., 6(1 E)(2018), 1035 1042 ISSN: 2347-1557 Available Online: http://ijmaa.in/ International Journal 2347-1557 of Mathematics Applications And its ISSN: International Journal of Mathematics
More informationAnswer: A. Answer: C. 3. If (G,.) is a group such that a2 = e, a G, then G is A. abelian group B. non-abelian group C. semi group D.
1. The set of all real numbers under the usual multiplication operation is not a group since A. zero has no inverse B. identity element does not exist C. multiplication is not associative D. multiplication
More informationTYPE-2 FUZZY G-TOLERANCE RELATION AND ITS PROPERTIES
International Journal of Analysis and Applications ISSN 229-8639 Volume 5, Number 2 (207), 72-78 DOI: 8924/229-8639-5-207-72 TYPE-2 FUZZY G-TOLERANCE RELATION AND ITS PROPERTIES MAUSUMI SEN,, DHIMAN DUTTA
More informationON FUZZY TOPOLOGICAL BCC-ALGEBRAS 1
Discussiones Mathematicae General Algebra and Applications 20 (2000 ) 77 86 ON FUZZY TOPOLOGICAL BCC-ALGEBRAS 1 Wies law A. Dudek Institute of Mathematics Technical University Wybrzeże Wyspiańskiego 27,
More informationAnti Q-Fuzzy Right R -Subgroup of Near-Rings with Respect to S-Norms
International Journal of Fuzzy Mathematics and Systems. ISSN 2248-9940 Volume 2, Number 2 (2012), pp. 171-177 Research India Publications http://www.ripublication.com Anti Q-Fuzzy Right R -Subgroup of
More informationA GENERALIZATION OF BI IDEALS IN SEMIRINGS
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874, ISSN (o) 2303-4955 www.imvibl.org /JOURNALS / BULLETIN Vol. 8(2018), 123-133 DOI: 10.7251/BIMVI1801123M Former BULLETIN
More informationWe begin with some definitions which apply to sets in general, not just groups.
Chapter 8 Cosets In this chapter, we develop new tools which will allow us to extend to every finite group some of the results we already know for cyclic groups. More specifically, we will be able to generalize
More informationHomomorphism on T Anti-Fuzzy Ideals of Ring
International Journal o Computational Science and Mathematics. ISSN 0974-3189 Volume 8, Number 1 (2016), pp. 35-48 International esearch Publication House http://www.irphouse.com Homomorphism on T nti-fuzzy
More informationREFLEXIVITY OF THE SPACE OF MODULE HOMOMORPHISMS
REFLEXIVITY OF THE SPACE OF MODULE HOMOMORPHISMS JANKO BRAČIČ Abstract. Let B be a unital Banach algebra and X, Y be left Banach B-modules. We give a sufficient condition for reflexivity of the space of
More informationInternational Journal of Mathematical Archive-7(1), 2016, Available online through ISSN
International Journal of Mathematical Archive-7(1), 2016, 200-208 Available online through www.ijma.info ISSN 2229 5046 ON ANTI FUZZY IDEALS OF LATTICES DHANANI S. H.* Department of Mathematics, K. I.
More informationCOMBINATORIAL GROUP THEORY NOTES
COMBINATORIAL GROUP THEORY NOTES These are being written as a companion to Chapter 1 of Hatcher. The aim is to give a description of some of the group theory required to work with the fundamental groups
More informationOn Regularity of Incline Matrices
International Journal of Algebra, Vol. 5, 2011, no. 19, 909-924 On Regularity of Incline Matrices A. R. Meenakshi and P. Shakila Banu Department of Mathematics Karpagam University Coimbatore-641 021, India
More informationFuzzy congruence relations on nd-groupoids
Proceedings of the International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2008 13 17 June 2008. Fuzzy congruence relations on nd-groupoids P. Cordero 1, I.
More informationConstructing Fuzzy Subgroups of Symmetric Groups S 4
International Journal of Algebra, Vol 6, 2012, no 1, 23-28 Constructing Fuzzy Subgroups of Symmetric Groups S 4 R Sulaiman Department of Mathematics, Faculty of Mathematics and Sciences Universitas Negeri
More information(Think: three copies of C) i j = k = j i, j k = i = k j, k i = j = i k.
Warm-up: The quaternion group, denoted Q 8, is the set {1, 1, i, i, j, j, k, k} with product given by 1 a = a 1 = a a Q 8, ( 1) ( 1) = 1, i 2 = j 2 = k 2 = 1, ( 1) a = a ( 1) = a a Q 8, (Think: three copies
More informationStrong - Bi Near Subtraction Semigroups
International Journal of Mathematics Research. ISSN 0976-5840 Volume 8, Number 3 (2016), pp. 207-212 International Research Publication House http://www.irphouse.com Strong - Bi Near Subtraction Semigroups
More informationDERIVATIONS. Introduction to non-associative algebra. Playing havoc with the product rule? BERNARD RUSSO University of California, Irvine
DERIVATIONS Introduction to non-associative algebra OR Playing havoc with the product rule? PART VI COHOMOLOGY OF LIE ALGEBRAS BERNARD RUSSO University of California, Irvine FULLERTON COLLEGE DEPARTMENT
More informationPacific Journal of Mathematics
Pacific Journal of Mathematics INVERSION INVARIANT ADDITIVE SUBGROUPS OF DIVISION RINGS DANIEL GOLDSTEIN, ROBERT M. GURALNICK, LANCE SMALL AND EFIM ZELMANOV Volume 227 No. 2 October 2006 PACIFIC JOURNAL
More informationSets and Motivation for Boolean algebra
SET THEORY Basic concepts Notations Subset Algebra of sets The power set Ordered pairs and Cartesian product Relations on sets Types of relations and their properties Relational matrix and the graph of
More informationA Study on Intuitionistic Fuzzy Number Group
International Journal of Fuzzy Mathematics and Systems. ISSN 2248-9940 Volume 2, Number 3 (2012), pp. 269-277 Research India Publications http://www.ripublication.com Study on Intuitionistic Fuzzy Number
More information(, q)-fuzzy Ideals of BG-Algebra
International Journal of Algebra, Vol. 5, 2011, no. 15, 703-708 (, q)-fuzzy Ideals of BG-Algebra D. K. Basnet Department of Mathematics, Assam University, Silchar Assam - 788011, India dkbasnet@rediffmail.com
More informationProperties of intuitionistic fuzzy line graphs
16 th Int. Conf. on IFSs, Sofia, 9 10 Sept. 2012 Notes on Intuitionistic Fuzzy Sets Vol. 18, 2012, No. 3, 52 60 Properties of intuitionistic fuzzy line graphs M. Akram 1 and R. Parvathi 2 1 Punjab University
More informationSpectrum of fuzzy prime filters of a 0 - distributive lattice
Malaya J. Mat. 342015 591 597 Spectrum of fuzzy prime filters of a 0 - distributive lattice Y. S. Pawar and S. S. Khopade a a Department of Mathematics, Karmaveer Hire Arts, Science, Commerce & Education
More informationFuzzy Function: Theoretical and Practical Point of View
EUSFLAT-LFA 2011 July 2011 Aix-les-Bains, France Fuzzy Function: Theoretical and Practical Point of View Irina Perfilieva, University of Ostrava, Inst. for Research and Applications of Fuzzy Modeling,
More informationFuzzy M-solid subvarieties
International Journal of Algebra, Vol. 5, 2011, no. 24, 1195-1205 Fuzzy M-Solid Subvarieties Bundit Pibaljommee Department of Mathematics, Faculty of Science Khon kaen University, Khon kaen 40002, Thailand
More informationFuzzy Dot Subalgebras and Fuzzy Dot Ideals of B-algebras
Journal of Uncertain Systems Vol.8, No.1, pp.22-30, 2014 Online at: www.jus.org.uk Fuzzy Dot Subalgebras and Fuzzy Dot Ideals of B-algebras Tapan Senapati a,, Monoranjan Bhowmik b, Madhumangal Pal c a
More informationIntuitionistic L-Fuzzy Rings. By K. Meena & K. V. Thomas Bharata Mata College, Thrikkakara
Global Journal of Science Frontier Research Mathematics and Decision Sciences Volume 12 Issue 14 Version 1.0 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals
More informationA Note on the Inverse Limits of Linear Algebraic Groups
International Journal of Algebra, Vol. 5, 2011, no. 19, 925-933 A Note on the Inverse Limits of Linear Algebraic Groups Nadine J. Ghandour Math Department Lebanese University Nabatieh, Lebanon nadine.ghandour@liu.edu.lb
More informationInterpolation of Fuzzy if-then rules in context of Zadeh's Z-numbers P.Rani 1, G.Velammal 2 1
American International Journal of Research in Science, Technology, Engineering & Mathematics Available online at http://www.iasir.net ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629
More information370 Y. B. Jun generate an LI-ideal by both an LI-ideal and an element. We dene a prime LI-ideal, and give an equivalent condition for a proper LI-idea
J. Korean Math. Soc. 36 (1999), No. 2, pp. 369{380 ON LI-IDEALS AND PRIME LI-IDEALS OF LATTICE IMPLICATION ALGEBRAS Young Bae Jun Abstract. As a continuation of the paper [3], in this paper we investigate
More informationarxiv: v1 [math.ra] 2 Mar 2008 Victor Bovdi, Tibor Rozgonyi 1
ON THE UNITARY SUBGROUP OF MODULAR GROUP ALGEBRAS arxiv:0803.0118v1 [math.ra] 2 Mar 2008 Victor Bovdi, Tibor Rozgonyi 1 Abstract. It this note we investigate the structure of the group of σ-unitary units
More informationHereditary right Jacobson radicals of type-1(e) and 2(e) for right near-rings
An. Şt. Univ. Ovidius Constanţa Vol. 21(1), 2013, 1 14 Hereditary right Jacobson radicals of type-1(e) and 2(e) for right near-rings Ravi Srinivasa Rao and K. Siva Prasad Abstract Near-rings considered
More informationOn Neutrosophic Semi-Open sets in Neutrosophic Topological Spaces
On Neutrosophic Semi-Open sets in Neutrosophic Topological Spaces P. Iswarya#1, Dr. K. Bageerathi*2 # Assistant Professor, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur,
More informationPseudo-Valuation Maps and Pseudo-Valuation Domains
Applied Mathematical Sciences, Vol. 7, 2013, no. 17, 799-805 HIKARI Ltd, www.m-hikari.com Pseudo-Valuation Maps and Pseudo-Valuation Domains Waheed Ahmad Khan 1 and Abdelghani Taouti 2 1 Department of
More informationPart 1. For any A-module, let M[x] denote the set of all polynomials in x with coefficients in M, that is to say expressions of the form
Commutative Algebra Homework 3 David Nichols Part 1 Exercise 2.6 For any A-module, let M[x] denote the set of all polynomials in x with coefficients in M, that is to say expressions of the form m 0 + m
More informationAnti fuzzy ideals of ordered semigroups
International Research Journal of Applied and Basic Sciences 2014 Available online at www.irjabs.com ISSN 2251-838X / Vol, 8 (1): 21-25 Science Explorer Publications Anti fuzzy ideals of ordered semigroups
More informationTRANSITIVE AND ABSORBENT FILTERS OF LATTICE IMPLICATION ALGEBRAS
J. Appl. Math. & Informatics Vol. 32(2014), No. 3-4, pp. 323-330 http://dx.doi.org/10.14317/jami.2014.323 TRANSITIVE AND ABSORBENT FILTERS OF LATTICE IMPLICATION ALGEBRAS M. SAMBASIVA RAO Abstract. The
More informationSome Aspects of 2-Fuzzy 2-Normed Linear Spaces
BULLETIN of the Malaysian Mathematical Sciences Society http://math.usm.my/bulletin Bull. Malays. Math. Sci. Soc. (2) 32(2) (2009), 211 221 Some Aspects of 2-Fuzzy 2-Normed Linear Spaces 1 R. M. Somasundaram
More informationGroups Subgroups Normal subgroups Quotient groups Homomorphisms Cyclic groups Permutation groups Cayley s theorem Class equations Sylow theorems
Group Theory Groups Subgroups Normal subgroups Quotient groups Homomorphisms Cyclic groups Permutation groups Cayley s theorem Class equations Sylow theorems Groups Definition : A non-empty set ( G,*)
More informationBulletin of the Transilvania University of Braşov Vol 10(59), No Series III: Mathematics, Informatics, Physics, 67-82
Bulletin of the Transilvania University of Braşov Vol 10(59), No. 1-2017 Series III: Mathematics, Informatics, Physics, 67-82 IDEALS OF A COMMUTATIVE ROUGH SEMIRING V. M. CHANDRASEKARAN 3, A. MANIMARAN
More informationThe Number of Fuzzy Subgroups of Group Defined by A Presentation
International Journal of Algebra, Vol 5, 2011, no 8, 375-382 The Number of Fuzzy Subgroups of Group Defined by A Presentation Raden Sulaiman Department of Mathematics, Faculty of Mathematics and Sciences
More informationIDEALS AND THEIR FUZZIFICATIONS IN IMPLICATIVE SEMIGROUPS
International Journal of Pure and Applied Mathematics Volume 104 No. 4 2015, 543-549 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v104i4.6
More informationInternational Mathematical Forum, 3, 2008, no. 39, Kyung Ho Kim
International Mathematical Forum, 3, 2008, no. 39, 1907-1914 On t-level R-Subgroups of Near-Rings Kyung Ho Kim Department of Mathematics, Chungju National University Chungju 380-702, Korea ghkim@cjnu.ac.kr
More informationComplete and Fuzzy Complete d s -Filter
International Journal of Mathematical Analysis Vol. 11, 2017, no. 14, 657-665 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2017.7684 Complete and Fuzzy Complete d s -Filter Habeeb Kareem
More informationFuzzy Sequences in Metric Spaces
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 15, 699-706 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4262 Fuzzy Sequences in Metric Spaces M. Muthukumari Research scholar, V.O.C.
More information3.2 Subspace. Definition: If S is a non-empty subset of a vector space V, and S satisfies the following conditions: (i).
. ubspace Given a vector spacev, it is possible to form another vector space by taking a subset of V and using the same operations (addition and multiplication) of V. For a set to be a vector space, it
More informationIntuitionistic Fuzzy Hyperideals in Intuitionistic Fuzzy Semi-Hypergroups
International Journal of Algebra, Vol. 6, 2012, no. 13, 617-636 Intuitionistic Fuzzy Hyperideals in Intuitionistic Fuzzy Semi-Hypergroups K. S. Abdulmula and A. R. Salleh School of Mathematical Sciences,
More informationRough G-modules and their properties
Advances in Fuzzy Mathematics ISSN 0973-533X Volume, Number 07, pp 93-00 Research India Publications http://wwwripublicationcom Rough G-modules and their properties Paul Isaac and Ursala Paul Department
More informationFUZZY BCK-FILTERS INDUCED BY FUZZY SETS
Scientiae Mathematicae Japonicae Online, e-2005, 99 103 99 FUZZY BCK-FILTERS INDUCED BY FUZZY SETS YOUNG BAE JUN AND SEOK ZUN SONG Received January 23, 2005 Abstract. We give the definition of fuzzy BCK-filter
More informationA Note on Linear Homomorphisms. in R-Vector Spaces
International Journal of Algebra, Vol. 5, 2011, no. 28, 1355-1362 A Note on Linear Homomorphisms in R-Vector Spaces K. Venkateswarlu Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia
More informationG. de Cooman E. E. Kerre Universiteit Gent Vakgroep Toegepaste Wiskunde en Informatica
AMPLE FIELDS G. de Cooman E. E. Kerre Universiteit Gent Vakgroep Toegepaste Wiskunde en Informatica In this paper, we study the notion of an ample or complete field, a special case of the well-known fields
More informationON STRUCTURE AND COMMUTATIVITY OF NEAR - RINGS
Proyecciones Vol. 19, N o 2, pp. 113-124, August 2000 Universidad Católica del Norte Antofagasta - Chile ON STRUCTURE AND COMMUTATIVITY OF NEAR - RINGS H. A. S. ABUJABAL, M. A. OBAID and M. A. KHAN King
More informationM. Suraiya Begum, M. Sheik John IJSRE Volume 4 Issue 6 June 2016 Page 5466
Volume 4 Issue 06 June-2016 Pages-5466-5470 ISSN(e):2321-7545 Website: http://ijsae.in DOI: http://dx.doi.org/10.18535/ijsre/v4i06.06 Soft g*s Closed Sets in Soft Topological Spaces Authors M. Suraiya
More informationMeasurement and Research Department Reports
Measurement and Research Department Reports 2005-2 FUZZY SET THEORY PROBABILITY THEORY? A COMMENT ON MEMBERSHIP FUNCTIONS AND PROBABILITY MEASURES OF FUZZY SETS. Gunter Maris cito, national institute for
More informationA Study on Lattice Ordered Fuzzy Soft Group
International Journal of Applied Mathematical Sciences ISSN 0973-0176 Volume 9, Number 1 (2016), pp. 1-10 Research India Publications http://www.ripublication.com A Study on Lattice Ordered Fuzzy Soft
More informationON BP -ALGEBRAS. Sun Shin Ahn, Jeong Soon Han
Hacettepe Journal of Mathematics and Statistics Volume 42 (5) (2013), 551 557 ON BP -ALGEBRAS Sun Shin Ahn, Jeong Soon Han Received 06 : 05 : 2011 : Accepted 25 : 11 : 2012 Abstract In this paper, we introduce
More informationAn Introduction to Fuzzy Soft Graph
Mathematica Moravica Vol. 19-2 (2015), 35 48 An Introduction to Fuzzy Soft Graph Sumit Mohinta and T.K. Samanta Abstract. The notions of fuzzy soft graph, union, intersection of two fuzzy soft graphs are
More informationLATTICE PROPERTIES OF T 1 -L TOPOLOGIES
RAJI GEORGE AND T. P. JOHNSON Abstract. We study the lattice structure of the set Ω(X) of all T 1 -L topologies on a given set X. It is proved that Ω(X) has dual atoms (anti atoms) if and only if membership
More informationLie Ideals and Generalized Derivations. in -Prime Rings - II
International Journal of Algebra, Vol. 6, 2012, no. 29, 1419 1429 Lie Ideals and Generalized Derivations in -Prime Rings - II M. S. Khan Department of Mathematics and Statistics Faculty of Science, Sultan
More informationInternational Journal of Algebra, Vol. 4, 2010, no. 2, S. Uma
International Journal of Algebra, Vol. 4, 2010, no. 2, 71-79 α 1, α 2 Near-Rings S. Uma Department of Mathematics Kumaraguru College of Technology Coimbatore, India psumapadma@yahoo.co.in R. Balakrishnan
More informationON FUZZY IDEALS OF PSEUDO MV -ALGEBRAS
Discussiones Mathematicae General Algebra and Applications 28 (2008 ) 63 75 ON FUZZY IDEALS OF PSEUDO MV -ALGEBRAS Grzegorz Dymek Institute of Mathematics and Physics University of Podlasie 3 Maja 54,
More informationAvailable Online through
Available Online through ISSN: 0975-766X CODEN: IJPTFI Research Article www.ijptonline.com NORMAL VAGUE IDEALS OF A Γ-NEAR RING S.Ragamayi* Department of Mathematics, K L University, Vaddeswaram, Guntur,
More informationQ-cubic ideals of near-rings
Inter national Journal of Pure and Applied Mathematics Volume 113 No. 10 2017, 56 64 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Q-cubic ideals
More informationSF2729 GROUPS AND RINGS LECTURE NOTES
SF2729 GROUPS AND RINGS LECTURE NOTES 2011-03-01 MATS BOIJ 6. THE SIXTH LECTURE - GROUP ACTIONS In the sixth lecture we study what happens when groups acts on sets. 1 Recall that we have already when looking
More informationStrong Deterministic Fuzzy Automata
Volume-5, Issue-6, December-2015 International Journal of Engineering and Management Research Page Number: 77-81 Strong Deterministic Fuzzy Automata A.Jeyanthi 1, B.Stalin 2 1 Faculty, Department of Mathematics,
More informationOn Fuzzy Dot Subalgebras of d-algebras
International Mathematical Forum, 4, 2009, no. 13, 645-651 On Fuzzy Dot Subalgebras of d-algebras Kyung Ho Kim Department of Mathematics Chungju National University Chungju 380-702, Korea ghkim@cjnu.ac.kr
More informationANNIHILATOR IDEALS IN ALMOST SEMILATTICE
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874, ISSN (o) 2303-4955 www.imvibl.org /JOURNALS / BULLETIN Vol. 7(2017), 339-352 DOI: 10.7251/BIMVI1702339R Former BULLETIN
More informationFinite groups determined by an inequality of the orders of their elements
Publ. Math. Debrecen 80/3-4 (2012), 457 463 DOI: 10.5486/PMD.2012.5168 Finite groups determined by an inequality of the orders of their elements By MARIUS TĂRNĂUCEANU (Iaşi) Abstract. In this note we introduce
More informationOn Fuzzy Semi-Pre-Generalized Closed Sets
BULLETIN of the Malaysian Mathematical Sciences Society http://math.usm.my/bulletin Bull. Malays. Math. Sci. Soc. (2) 28(1) (2005), 19 30 On Fuzzy Semi-Pre-Generalized Closed Sets 1 R.K. Saraf, 2 Govindappa
More informationα-fuzzy Quotient Modules
International Mathematical Forum, 4, 2009, no. 32, 1555-1562 α-fuzzy Quotient Modules S. K. Bhambri and Pratibha Kumar Department of Mathematics Kirori Mal College (University of Delhi) Delhi-110 007,
More information